Virial equation of state

From SklogWiki
Revision as of 10:32, 8 April 2011 by Carl McBride (talk | contribs) (Added mention of PIMC calculations)
Jump to navigation Jump to search

The virial equation of state is used to describe the behavior of diluted gases. It is usually written as an expansion of the compressibility factor, , in terms of either the density or the pressure. Such an expansion was first introduced in 1885 by Thiesen [1] and extensively studied by Heike Kamerlingh Onnes [2] [3], and mathematically by Ursell [4]. One has

.

where

  • is the pressure
  • is the volume
  • is the number of molecules
  • is the temperature
  • is the Boltzmann constant
  • is the (number) density
  • is called the k-th virial coefficient

Virial coefficients

The second virial coefficient represents the initial departure from ideal-gas behaviour

where is Avogadros number and and are volume elements of two different molecules in configuration space.

One can write the third virial coefficient as

where f is the Mayer f-function (see also: Cluster integrals). See also [5]

Convergence

For a commentary on the convergence of the virial equation of state see [6] and section 3 of [7].

Quantum virial coefficients

Using the path integral formulation one can also calculate the virial coefficients of quantum systems [8].

References

Related reading